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A169630 a(n) = n times the square of Fibonacci(n). 6

%I #45 Jan 02 2023 12:30:47

%S 0,1,2,12,36,125,384,1183,3528,10404,30250,87131,248832,705757,

%T 1989806,5581500,15586704,43356953,120187008,332134459,915304500,

%U 2516113236,6900949462,18888143927,51599794176,140718765625,383142771674

%N a(n) = n times the square of Fibonacci(n).

%H Vincenzo Librandi, <a href="/A169630/b169630.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Baron, H. Prodinger, R. F. Tichy, F. T. Boesch, J. F. Wang, <a href="http://www.fq.math.ca/Scanned/23-3/baron.pdf">The number of spanning trees in the square of a cycle</a>, Fibonacci Quart. 23 (1985), no. 3, 258-264 [<a href="http://www.ams.org/mathscinet-getitem?mr=806296">MR0806296</a>]

%H R. Guy, <a href="http://list.seqfan.eu/oldermail/seqfan/2010-March/003959.html">Q on papers by Kleitman, Baron et al.</a>, SeqFan list, Mar 2010

%H D. J. Kleitman, B. Golden, <a href="http://www.jstor.org/stable/2319131">Counting trees in a certain class of graphs</a>, Amer. Math. Monthly 82 (1975), 40-44.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-10,0,4,-1)

%F a(n) = A045925(n)*A000045(n) = n*A007598(n) = n *(A000045(n))^2.

%F a(n) = 4*a(n-1) -10*a(n-3) +4*a(n-5) -a(n-6).

%F G.f.: x*(1-2*x+4*x^2-2*x^3+x^4)/ ((1+x)^2 * (x^2-3*x+1)^2).

%p A169630 := proc(n) n*(combinat[fibonacci](n))^2 ; end proc:

%t CoefficientList[Series[x*(1 - 2*x + 4*x^2 - 2*x^3 + x^4)/((1 + x)^2*(x^2 - 3*x + 1)^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)

%t Table[n Fibonacci[n]^2,{n,0,30}] (* or *) LinearRecurrence[{4,0,-10,0,4,-1},{0,1,2,12,36,125},30] (* _Harvey P. Dale_, Jul 07 2017 *)

%o (Magma) I:=[0,1,2,12,36,125]; [n le 6 select I[n] else 4*Self(n-1)-10*Self(n-3)+4*Self(n-5)-Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Dec 19 2012

%o (Haskell)

%o a169630 n = a007598 n * n -- _Reinhard Zumkeller_, Sep 01 2013

%o (PARI) vector(40, n, n--; n*fibonacci(n)^2) \\ _Michel Marcus_, Jul 09 2015

%Y Cf. A000045, A007598, A045925, A282464 (partial sums).

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Mar 13 2010

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)